Hashtags create a clickable link in most Twitter clients [and on the website] and are often used to attach to events without being a logical word but are not required for search results.

In that first tweet you pointed to there are a number of random seeming hashtags but each refers to a topic that is being talked about. Someone searching on those trends won't find the other tweets.

Now for some strategy it's important to realize that most user's don't search out information on a topic but rather find it from people they follow. However hashtags make it more likely that someone will jump into the "stream" and being attached makes sense but that doesn't mean you should cram in a dozen hashtags, it just makes your tweets look like spam.